"Chris Kyle's death seems to confirm that 'he who lives by the sword dies by the sword.' Treating PTSD at a gun range doesn't make sense," former Texas Republican Rep. Ron Paul tweeted on Monday.

But what seems like common sense to some is viewed by others as another assault on the Second Amendment.

Those types of concerns are what prompted a heated debate last December as lawmakers worked to approve a defense policy bill.

Republican Sen. Tom Coburn pushed and then backed away from an amendment to block the Department of Veteran Affairs from automatically entering the names of veterans deemed "mentally incompetent" to handle their finances from having their names entered into a national background check system, thereby blocking them from gun ownership.

Instead, the Oklahoma physician wanted those case decided by a judge rather than a federal agency unless those veterans had been "found by a judicial authority to be a danger to themselves or to others."

"We're not asking for anything big," Coburn said at the time. "We're just saying that if you're going to take away the Second Amendment rights -- they ought to have it adjudicated, rather than mandated by someone who's unqualified to state that they should lose their rights."

New York Democratic Sen. Chuck Schumer pushed back argued that "you should not have a gun" whether "you are a veteran or not and you have been judged to be mentally infirm."

National Rifle Association President David Keene said at a recent media event that his organization supports reforms that would make it tougher for mentally ill people to get guns.

Federal law makes it illegal to sell or give a firearm to anyone who "has been adjudicated as a mental defective or has been committed to any mental institution."

Statistics from the FBI's National Instant Criminal Background Check System (NICS) show about 1 percent of applicants who failed a background check over the past 14 years, or 10,180 people, were turned down for reasons related to mental health.

Overall rejections represented a fraction of prospective gun sales and most involved applicants with criminal records.

Federally licensed gun shops must use the National Instant Criminal Background Check System, or NICS. Private sellers and gun shows have no background check requirement.

But information in the national background check system is incomplete, particularly involving mental health records, investigations have found.

Critics blame what they call a huge legal loophole, according to one study.

"PTSD is rarely associated with homicidal violence," Michael Welner, a forensic psychiatrist who has worked on cases of Iraq and Afghanistan veterans charged with violent crimes, told CNN's Soledad O'Brien.

"PTSD is very commonly associated with a number of other conditions that are regularly attached to violence, alcoholism, personality disorder, depression. So diagnostically, PTSD may be relevant and it may just be part of the picture, including traumatic brain injury," Welner said.

Expanding some background checks is under consideration in Congress as lawmakers respond to public and political pressure for stricter laws following December's shooting massacre at a Connecticut elementary school.

Possible steps include better monitoring of people with mental illness to prevent them from obtaining firearms.